"""simple docstring"""


from collections.abc import Iterable
from typing import Any






class   __UpperCAmelCase		:

				def __init__( self      ,					_lowerCamelCase = None ):
										lowerCamelCase__   =value
										lowerCamelCase__   =None  # Added in order to delete a node easier
										lowerCamelCase__   =None
										lowerCamelCase__   =None






				def __repr__( self ):
										from pprint import pformat

										if self.left is None and self.right is None:
																return str(self.value )
										return pformat({F'''{self.value}''': (self.left, self.right)}      ,					indent=1 )






class   __UpperCAmelCase		:

				def __init__( self      ,					_lowerCamelCase = None ):
										lowerCamelCase__   =root

				def __str__( self ):
										return str(self.root )

				def 						_a      ( self      ,					_lowerCamelCase      ,					_lowerCamelCase ):
										if new_children is not None:  # reset its kids
																lowerCamelCase__   =node.parent
										if node.parent is not None:  # reset its parent
																if self.is_right(_lowerCamelCase ):  # If it is the right children
																						lowerCamelCase__   =new_children
																else:
																						lowerCamelCase__   =new_children
										else:
																lowerCamelCase__   =new_children

				def 						_a      ( self      ,					_lowerCamelCase ):
										if node.parent and node.parent.right:
																return node == node.parent.right
										return False

				def 						_a      ( self ):
										return self.root is None

				def 						_a      ( self      ,					_lowerCamelCase ):
										lowerCamelCase__   =Node(_lowerCamelCase )  # create a new Node
										if self.empty():  # if Tree is empty
																lowerCamelCase__   =new_node  # set its root
										else:  # Tree is not empty
																lowerCamelCase__   =self.root  # from root
																if parent_node is None:
																						return
																while True:  # While we don't get to a leaf
																						if value < parent_node.value:  # We go left
																												if parent_node.left is None:
																																		lowerCamelCase__   =new_node  # We insert the new node in a leaf
																																		break
																												else:
																																		lowerCamelCase__   =parent_node.left
																						else:
																												if parent_node.right is None:
																																		lowerCamelCase__   =new_node
																																		break
																												else:
																																		lowerCamelCase__   =parent_node.right
																lowerCamelCase__   =parent_node

				def 						_a      ( self      ,					*_lowerCamelCase ):
										for value in values:
																self.__insert(_lowerCamelCase )

				def 						_a      ( self      ,					_lowerCamelCase ):
										if self.empty():
																raise IndexError("Warning: Tree is empty! please use another." )
										else:
																lowerCamelCase__   =self.root
																# use lazy evaluation here to avoid NoneType Attribute error
																while node is not None and node.value is not value:
																						lowerCamelCase__   =node.left if value < node.value else node.right
																return node

				def 						_a      ( self      ,					_lowerCamelCase = None ):
										if node is None:
																if self.root is None:
																						return None
																lowerCamelCase__   =self.root

										if not self.empty():
																while node.right is not None:
																						lowerCamelCase__   =node.right
										return node

				def 						_a      ( self      ,					_lowerCamelCase = None ):
										if node is None:
																lowerCamelCase__   =self.root
										if self.root is None:
																return None
										if not self.empty():
																lowerCamelCase__   =self.root
																while node.left is not None:
																						lowerCamelCase__   =node.left
										return node

				def 						_a      ( self      ,					_lowerCamelCase ):
										lowerCamelCase__   =self.search(_lowerCamelCase )  # Look for the node with that label
										if node is not None:
																if node.left is None and node.right is None:  # If it has no children
																						self.__reassign_nodes(_lowerCamelCase      ,					_lowerCamelCase )
																elif node.left is None:  # Has only right children
																						self.__reassign_nodes(_lowerCamelCase      ,					node.right )
																elif node.right is None:  # Has only left children
																						self.__reassign_nodes(_lowerCamelCase      ,					node.left )
																else:
																						lowerCamelCase__   =self.get_max(
																						    node.left )  # Gets the max value of the left branch
																						self.remove(tmp_node.value )  # type: ignore
																						lowerCamelCase__   =(
																						    tmp_node.value  # type: ignore
																						)  # Assigns the value to the node to delete and keep tree structure

				def 						_a      ( self      ,					_lowerCamelCase ):
										if node is not None:
																yield node  # Preorder Traversal
																yield from self.preorder_traverse(node.left )
																yield from self.preorder_traverse(node.right )

				def 						_a      ( self      ,					_lowerCamelCase=None ):
										if traversal_function is None:
																return self.preorder_traverse(self.root )
										else:
																return traversal_function(self.root )

				def 						_a      ( self      ,					_lowerCamelCase      ,					_lowerCamelCase ):
										if node:
																self.inorder(_lowerCamelCase      ,					node.left )
																arr.append(node.value )
																self.inorder(_lowerCamelCase      ,					node.right )






				def 						_a      ( self      ,					_lowerCamelCase      ,					_lowerCamelCase ):
										lowerCamelCase__   =[]
										self.inorder(_lowerCamelCase      ,					_lowerCamelCase )  # append all values to list using inorder traversal
										return arr[k - 1]





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   list[Node]:




						'''simple docstring'''



						lowerCamelCase__   =[]
						if curr_node is not None:
												lowerCamelCase__   =postorder(curr_node.left							) + postorder(curr_node.right							) + [curr_node]
						return node_list





def      lowerCamelCase_					(   )				->   None:




						'''simple docstring'''



						lowerCamelCase__   =(8, 3, 6, 1, 10, 14, 13, 4, 7)
						lowerCamelCase__   =BinarySearchTree()
						for i in testlist:
												t.insert(__lowerCAmelCase							)

						# Prints all the elements of the list in order traversal
						print(__lowerCAmelCase							)

						if t.search(6							) is not None:
												print("The value 6 exists"							)
						else:
												print("The value 6 doesn't exist"							)

						if t.search(-1							) is not None:
												print("The value -1 exists"							)
						else:
												print("The value -1 doesn't exist"							)

						if not t.empty():
												print("Max Value: "  ,       t.get_max().value							)  # type: ignore
												print("Min Value: "  ,       t.get_min().value							)  # type: ignore

						for i in testlist:
												t.remove(__lowerCAmelCase							)
												print(__lowerCAmelCase							)


if __name__ == "__main__":
	import doctest

	doctest.testmod(verbose=True)



"""simple docstring"""


def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						def update_area_of_max_square(__lowerCAmelCase  ,       __lowerCAmelCase							) -> int:
												# BASE CASE
												if row >= rows or col >= cols:
																		return 0

												lowerCamelCase__   =update_area_of_max_square(__lowerCAmelCase  ,       col + 1							)
												lowerCamelCase__   =update_area_of_max_square(row + 1  ,       col + 1							)
												lowerCamelCase__   =update_area_of_max_square(row + 1  ,       __lowerCAmelCase							)

												if mat[row][col]:
																		lowerCamelCase__   =1 + min([right, diagonal, down]							)
																		lowerCamelCase__   =max(largest_square_area[0]  ,       __lowerCAmelCase							)
																		return sub_problem_sol
												else:
																		return 0

						lowerCamelCase__   =[0]
						update_area_of_max_square(0  ,       0							)
						return largest_square_area[0]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						def update_area_of_max_square_using_dp_array(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							) -> int:
												if row >= rows or col >= cols:
																		return 0
												if dp_array[row][col] != -1:
																		return dp_array[row][col]

												lowerCamelCase__   =update_area_of_max_square_using_dp_array(__lowerCAmelCase  ,       col + 1  ,       __lowerCAmelCase							)
												lowerCamelCase__   =update_area_of_max_square_using_dp_array(row + 1  ,       col + 1  ,       __lowerCAmelCase							)
												lowerCamelCase__   =update_area_of_max_square_using_dp_array(row + 1  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)

												if mat[row][col]:
																		lowerCamelCase__   =1 + min([right, diagonal, down]							)
																		lowerCamelCase__   =max(largest_square_area[0]  ,       __lowerCAmelCase							)
																		lowerCamelCase__   =sub_problem_sol
																		return sub_problem_sol
												else:
																		return 0

						lowerCamelCase__   =[0]
						lowerCamelCase__   =[[-1] * cols for _ in range(__lowerCAmelCase							)]
						update_area_of_max_square_using_dp_array(0  ,       0  ,       __lowerCAmelCase							)

						return largest_square_area[0]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						lowerCamelCase__   =[[0] * (cols + 1) for _ in range(rows + 1							)]
						lowerCamelCase__   =0
						for row in range(rows - 1  ,       -1  ,       -1							):
												for col in range(cols - 1  ,       -1  ,       -1							):
																		lowerCamelCase__   =dp_array[row][col + 1]
																		lowerCamelCase__   =dp_array[row + 1][col + 1]
																		lowerCamelCase__   =dp_array[row + 1][col]

																		if mat[row][col] == 1:
																								lowerCamelCase__   =1 + min(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
																								lowerCamelCase__   =max(dp_array[row][col]  ,       __lowerCAmelCase							)
																		else:
																								lowerCamelCase__   =0

						return largest_square_area





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						lowerCamelCase__   =[0] * (cols + 1)
						lowerCamelCase__   =[0] * (cols + 1)
						lowerCamelCase__   =0
						for row in range(rows - 1  ,       -1  ,       -1							):
												for col in range(cols - 1  ,       -1  ,       -1							):
																		lowerCamelCase__   =current_row[col + 1]
																		lowerCamelCase__   =next_row[col + 1]
																		lowerCamelCase__   =next_row[col]

																		if mat[row][col] == 1:
																								lowerCamelCase__   =1 + min(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
																								lowerCamelCase__   =max(current_row[col]  ,       __lowerCAmelCase							)
																		else:
																								lowerCamelCase__   =0
												lowerCamelCase__   =current_row

						return largest_square_area


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))


